We present detailed gas-phase chemical models for the envelope of the low-mass star-forming region IRAS 16293-2422. By considering both time- and space-dependent chemistry, these models are used to study both the physical structure proposed by Schoeier et al. (2002A&A...390.1001S), as well as the chemical evolution of this region. A new feature of our study is the use of a detailed, self-consistent radiative transfer model to translate the model abundances into line strengths and compare them directly with observations of a total of 76 transitions for 18 chemical species, and their isotopes. The model can reproduce many of the line strengths observed within 50%. The best fit is for times in the range of 3x103-3x104yrs and requires only minor modifications to our model for the high-mass star-forming region AFGL 2591. The ionization rate for the source may be higher than previously expected - either due to an enhanced cosmic-ray ionization rate, or, more probably, to the presence of X-ray induced ionization from the center. A significant fraction of the CO is found to desorb in the temperature range of 15-40K; below this temperature ∼90% or more of the CO is frozen out. The inability of the model to explain the HCS+, C2H, and OCS abundances suggests the importance of further laboratory studies of basic reaction rates. Finally, predictions of the abundances and spatial distributions of other species which could be observed by future facilities (e.g. Herschel-HIFI, SOFIA, millimeter arrays) are provided.